Domain: (−∞,−1]∪[1,∞),{x|x≤−1,x≥1}
Range: [−π2,0)∪(0,π2],{y∣∣−π2≤y≤π2,y≠0}
How to find and reach a domain?
Domain and domain To find the domain, solve the equation y = f (x), find the value of the independent variable x, and get the domain. To calculate the domain of a function, express x as x = g (y) and find the domain of g (y).
The domain of the specified function is a set of all real numbers except -4. The scope of a function also contains a set of dependent variable values that define a particular function. This is defined only if y is not equal to 2. Therefore, the range of the given function is (-∞, 2) U (2, ∞).
y = CSC (x) is the reciprocal of y = sin(x)so its domain and range are related to sine's domain and range.
Since the range of y = sin(x)is −1≤y≤1
we get that the range of y= CSC(x)
is y≤−1 or y≥1, which encompasses the reciprocal of every value in the range of sine.
The domain of y= CSC(x) is every value in the domain of sine with the exception of where sin(x)=0, since the reciprocal of 0 is undefined. So we solve sin(x)=0and get x=0+π⋅n where n∈Z. That means the domain of y=csc(x) is x∈R,x≠π⋅n, n∈Z.
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